Sound Field Synthesis with Acoustic Waves

TL;DR

The paper addresses accurate broadband sound-field synthesis on rigid device surfaces by decoupling room acoustics from device scattering. It introduces a decoupled framework that uses a plane-wave expansion $p(\omega,\mathbf{r}) = \sum_{l\in\Lambda} \alpha_l(\omega)\,\psi(\omega,\theta_l,\phi_l,\mathbf{r})$ for the room and a device dictionary $\mathcal{D}=\{\boldsymbol{\beta}_l(\omega)\}$ to capture scattering, combining them to form the total field on the device with $p_t(\omega,\theta,\phi,\mathbf{r}) = \psi(\omega,\theta,\phi,\mathbf{r}) + p_s(\omega,\theta,\phi,\mathbf{r})$. A sparse recovery approach solves for $\alpha_l(\omega)$ using measurements from a large microphone array, while RIRs are estimated via Wiener-Hopf $\hat{\mathbf{h}}(\omega) = \mathbf{S}_{xy}(\omega)/S_{xx}(\omega)$ and combined with source signals to synthesize responses, including background noise. Validation across multiple rooms and device geometries demonstrates accurate broadband rendering up to $8$ kHz, enabling cost-effective data generation and enhanced microphone-array processing. The framework is poised to significantly reduce hardware validation costs while providing a versatile, reusable representation of room-device acoustics, with potential extensions to near-field scenarios using spherical waves.

Abstract

We propose a practical framework to synthesize the broadband sound-field on a small rigid surface based on the physics of sound propagation. The sound-field is generated as a composite map of two components: the room component and the device component, with acoustic plane waves as the core tool for the generation. This decoupling of room and device components significantly reduces the problem complexity and provides accurate rendering of the sound-field. We describe in detail the theoretical foundations, and efficient procedures of the implementation. The effectiveness of the proposed framework is established through rigorous validation under different environment setups.

Figures (5)

• Figure 1: (top) Measured (solid line) and simulated (dotted line) total field of a microphone array mounted on a sphere of PW, (bottom) phase error, with azimuth = $150^\circ$, elevation = $90^\circ$.
• Figure 2: EigenMike reconstruction error versus the number of plane waves in the plane wave decomposition
• Figure 3: An example of frequency response of measured and synthetic RIR for a microphone array of size 4 on a slated sphere surface
• Figure 4: An example of impulse response of measured and synthetic for microphone array of size 4 on a slated sphere surface
• Figure 5: Cumulative density function (CDF) of the relative absolute FRR error